Mathematically calculating Wax Speed

[Zoey]

So I have been wondering for a while how to calculate what speed Wax can go via manipulating his mass. It is simple enough if we ignore Wind Resistance and all. But it gets more complicated including it. 

Ultimately though, I came to a conclusion. If we treat the change in mass as being by a factor of 1/a. Then the velocity following would be v₀a. 

But of course we know wind resistance still effects him, thus we have to take into account drag. 

 

Sqrt( [ma^2 * v^2 - 2aF]/m)

 

was my result. 

This actually reveals some interesting features of his velocity changes. Along with lower and upper bounds to where his mass changes allow him to move.

• (62kg, 13.8889m/s, store 25%) > (18.279 m/s)

I am having trouble finding an equation for the maximum possible velocity given his initial mass and velocity. But here are some examples. I am assuming a base 62kg for Waxillium, a surface area for drag of 0.95 m/s, air density of 1.225, and a Drag Coefficent of 1.15

• (62kg, 13.8889m/s) > (248.811 m/s at a = 30.981, or 2kg) [13.8889 is average car speed]
• (62kg, 1 m/s) > (18.98 m/s at a = 32.208)
• (62kg, e m/s) > (49.623 m/s at a = 31.374)

 

The formula for the points in which your speed just hits 0 are 2F/mv^2. This sets an upper and lower bound to how much you can store and have an effect, furthermore, past these peak points, ones velocity begins to decrease as one stores more into a metalmind. 

 

Formula with Terminal Velocity should be obvious, it is a simple modification which comes out as:

Sqrt({2[1/a * m]g} / pAc)

This one has no inherent limitations, and can increase and decrease without limit.

The fact that there is a limit to the degree in which you can speed up through changing mass does actually fit with what Brandon said in this WoB: (actually can one find the one I am thinking of, can't find it, but he did mention you can't just store a crapton of weight and go extremely fast)

Well here is this one for now: https://wob.coppermind.net/events/40/#e692

 

Another thing of note with this, is that while this preserves momentum, it increases kinetic energy. Which I would assume would have to come from somewhere. As I understand it. But we do know that Feruchemy isn't truly End-Neutral (https://wob.coppermind.net/events/2/#e171), it takes a bit of energy from the Spiritual Realm. Maybe this energy is able to give them more of a shove. 

Note: Image below assumes mass of 1kg, and initial velocity of 1m/s. This is just because this way it is smaller and looks nicer.